Entanglement properties of quantum polaritons

Exciton polaritons are coupled states of matter and light, originated by the strong interaction between an optical mode and semiconductor excitons. This interaction can be obtained also at a single-particle level, in which case it has been shown that a quantum treatment is mandatory. In this work we study the light-matter entanglement of polaritons from a fully quantum formalism including pumping and dissipation. We find that the entanglement is completely destroyed if the exciton and photon are tuned at the resonance condition, even under very low pumping rates. Instead, the best condition for maximizing entanglement and purity of the steady state is when the exciton and photon are out of resonance and when incoherent pumping exactly compensates the dissipation rate. In the presence of multiple quantum dots coupled to the light mode, matter-light entanglement survives only at larger detuning for a higher number of quantum dots considered.